# How do you use symbols to make the statement 9_45_9_8 = 49 true?

Mar 6, 2016

$9 + \frac{45}{9} \cdot 8 = 49$

#### Explanation:

In this case, you can use trial and error to get the desired value ($= 49$).

So for this I started with the operations done on 45 because I initially felt that it was the "outlier" among the values given. Note that you can start with any number that you are comfortable with.

You would not want to multiply 9 by 45 because it would give you a really big number, hence $9 \cdot 45$ is not an option. Moreover $\frac{9}{45}$ would give you a decimal value that cannot be reverted to whole number by 9 or 8 so this is also not an option. This leaves us with addition and subtraction for the 9_45 portion.

For the 45_9, we would not want to use multiplication for the same reason that we do not want $9 \cdot 45$. Dividing 45 by 9 seems to be a good option because it would reduce the two numbers to 5. Following this line of thought...

[Trial-and-Error Portion]
9_45_9_8 = 49
9_45/9_8 = 49
9_5_8 = 49

When you reach this part, it would be easier to decide which operations to use. Since you know that $9 \cdot 5 = 45$ and adding or subtracting 8 to 45 would not give you 49, you know that you should multiply 5 by 8 instead...

[Continuation of Solution]
9_5_8 = 49
9_5*8 = 49
9_40 = 49
9+40 = 49

Luckily in one try we were able to reach the answer, but most of the time you would need to use trial and error to arrive at the right combination of operations.

*The explanation may be confusing but feel free to comment or post questions in the comment section if you think that the explanation needs more elaboration then I'll try to reply asap :D